Gariboh clan

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The gariboh clan of rank-2 temperaments tempers out the gariboh comma, 3125/3087 ([0 -2 5 -3⟩).

Sirius

Subgroup: 3.5.7

Comma list: 3125/3087

Subgroup-val mapping: [⟨1 1 1], ⟨0 3 5]]

mapping generators: ~3, ~25/21

Optimal tunings:

• WE: ~3 = 1902.4455 ¢, ~25/21 = 293.7393 ¢
• CWE: ~3 = 1901.9550 ¢, ~25/21 = 293.7594 ¢

Optimal ET sequence: b6, b7, b13, b71, b84, b97, b110, b123, b136

Badness (Sintel): 0.213

Overview to extensions

The full 7-limit extensions' relation to sirius is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are diminished, ammonite, and maja. These temperaments are distributed into different family pages.

• Diminished (+36/35) → Diminished family
• Ammonite (+250/243) → Porcupine family
• Maja (+2430/2401) → Maja family

The others are weak extensions. Bohpier tempers out 245/243 with a 1/13-twelfth period. Kleiboh tempers out 1728/1715 with a 1/6-twelfth period. Passion tempers out 64/63, splitting the generator in six. Garibaldi tempers out 225/224. Quasitemp tempers out 875/864. Dodecacot tempers out 10976/10935. These split the generator in five. Trismegistus tempers out 1029/1024, splitting the generator in two with a 1/5-twelfth period. Submerged tempers out 525/512, splitting the generator in nine. Finally, semaja tempers out 6144/6125, splitting the generator in eleven.

Discussed elsewhere are:

• Garibaldi (+225/224) → Schismatic family
• Passion (+64/63) → Passion family
• Submerged (+525/512) → Avicennmic temperaments
• Dodecacot (+10976/10935) → Tetracot family
• Bohpier (+245/243) → Sensamagic clan
• Quasitemp (+875/864) → Keemic temperaments
• Trismegistus (+1029/1024) → Magic family
• Kleiboh (+1728/1715) → Kleismic family

Considered below is semaja. For no-twos extensions, see No-twos subgroup temperaments.

Semaja

See also: Llywelynsmic clan

Cryptically named by Petr Pařízek in 2011, semaja adds the porwell comma to the comma list, and may be described as the 37 & 53 temperament. Its ploidacot is gamma-19-cot (or alpha-heptaseph due to a much simpler 2.5.7-subgroup restriction). The name actually refers to the fact that two of its ~8/7 generator steps reach a ~13/10.

Subgroup: 2.3.5.7

Comma list: 3125/3087, 6144/6125

Mapping: [⟨1 -2 1 3], ⟨0 19 7 -1]]

mapping generators: ~2, ~8/7

Optimal tunings:

• WE: ~2 = 1199.4860 ¢, ~8/7 = 226.3864 ¢

error map: ⟨-0.514 +0.415 -2.123 +3.246]

• CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4697 ¢

error map: ⟨0.000 +0.970 -1.026 +4.704]

Optimal ET sequence: 16, 37, 53, 196d

Badness (Sintel): 2.71

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 3125/3087

Mapping: [⟨1 -2 1 3 1], ⟨0 19 7 -1 13]]

Optimal tunings:

• WE: ~2 = 1199.9818 ¢, ~8/7 = 226.4821 ¢
• CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4851 ¢

Optimal ET sequence: 16, 37, 53

Badness (Sintel): 1.98

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 169/168, 176/175, 275/273

Mapping: [⟨1 -2 1 3 1 2], ⟨0 19 7 -1 13 9]]

Optimal tunings:

• WE: ~2 = 1200.1020 ¢, ~8/7 = 226.4987 ¢
• CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4822 ¢

Optimal ET sequence: 16, 37, 53

Badness (Sintel): 1.35